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vodomira [7]
3 years ago
15

A curve passes through the point (0,7) and has the property that the slope of the curve at every point P is five times the y-coo

rdinate of P. What is the equation of the curve
Mathematics
1 answer:
iren [92.7K]3 years ago
8 0

Answer:

y(x) = 7e^(5x)

Step-by-step explanation:

The question says that the slope of the curve at every point P is five times the y-coordinate of P. This means that

dy/dx = 5y

Refer to solutions of differential equations, dy/dt = ky, being in the form of y(t) = y(0) e^(kt)

Using the above stated law now, we can relate to our equation, saying that

y(x) = y(0) e^(5x)

The point given from the question is, (0, 7). This also means that y(0) = 7. So finally, we can have

y(x) = 7e^(5x)

And that is our needed equation of the curve

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Triangle NLM is reflected over the line segment as
Vladimir [108]
NLM-CAB would be the right answer
3 0
2 years ago
The width of a rectangle is 12 inches more than the length. The perimeter is 76 inches. Find the width and the length.
stira [4]

Answer:

The length of the rectangle is 13 inches and its width (13 + 12) is 25 inches.

Step-by-step explanation:

You have to consider the formula of the perimeter = 2·length + 2·width.

If we call "x" to the length ⇒ width = x + 12 .

Perimeter = 2x + 2·(x + 12) ⇒ Perimeter = 2x + 2x + 24

⇒Perimeter = 4x + 24. ⇒ 76 = 4x + 24 ⇒ 76 - 24 = 4x ⇒52 = 4x

⇒ 52/4 = x ⇒ x = 13.

So, the length of the rectangle is 13 inches and its width (13 + 12) is 25 inches.

3 0
2 years ago
SOMEONE PLEASE HELP MEEE!!!! HOW DO YOU DO THIS
UkoKoshka [18]

Answer:

A. 162 m²

Step-by-step explanation:

==>Given:

Isosceles trapezoid with:

base a = 19m

base b = 35m

Perimeter = 74meters

==>Required:

Area of trapezoid

==>Solution:

Recall: the length of the legs of an isosceles trapezoid are equal.

Perimeter of isosceles trapezoid = sum of the parallel sides + 2(length of a leg of the trapezoid)

Let l = leg of trapezoid.

Perimeter = 74m

Sum of parallel sides = a+b = 19+35 = 54m

Thus,

74 = 54 + 2(l)

74 - 54 = 2(l)

20 = 2(l)

l = 20/2 = 10m

Let's find area:

Area = ½(a+b)*h

a = 19

b = 35

h = ?

Using Pythagorean theorem, let's find h as follows:

h² = l² - [(35-19)/2)²

h² = 10² - [16/2]²

h² = 100 - 64

h² = 36

h = √36 = 6m

Area = ½ x (a+b) × h

= ½ × (19+35) × 6

= ½ × 54 × 6

= 27 × 6

Area = 162m²

6 0
3 years ago
Someone please help! No link answer please :(
grandymaker [24]

Answer:

55 degrees (a)

Step-by-step explanation:

complementary means they equal 90 degrees

so 90-35= 55 degrees

3 0
3 years ago
Need help with 6,7,8,9,10,11,12,15
Ainat [17]

Answer:

6. 1.01 x -10^5

7. 6 x -10^14

8. 550,000

9. 60,700,000

10. 0.000204

11. 0.0004

12. 7,000,000,000,000 > 3,500,000,000

     7,000,000,000,000 (or 7 x 10^12) is greater by 2,000 times

15. 10^3 and 10^4

7 0
3 years ago
Read 2 more answers
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